Origin of chaos in nuclear spectra: role of symmetries

We investigate the role of symmetry as a possible origin of chaos in the nuclear shell model. For this purpose we disentangle purely geometrical effects due to spin and isospin coupling of the many–body states, from effects of the reduced two– body interaction. We compare a model without symmetry (the embedded two– body ensemble of random matrices) with the two–body random ensemble (TBRE) of the shell model. We show that in the TBRE, there is already considerable mixing of many–body states from only a single reduced two–body matrix element. This is particularly the case for a single j–shell and, in a shell model with subshells, for the many–body states which belong to the same partition (same number of nucleons in each of the subshells). We conclude that in the shell model, chaos is largely generated by symmetry. This mechanism differs considerably from that of the embedded ensemble.